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Number of permutations p of {1,...,n} such that |p(i+1)-p(i)| < k, k=2,...,n; T(n,k), read by rows.
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%I #19 Nov 20 2014 06:07:11

%S 2,2,6,2,12,24,2,20,72,120,2,34,180,480,720,2,56,428,1632,3600,5040,2,

%T 88,1042,5124,15600,30240,40320,2,136,2512,15860,61872,159840,282240,

%U 362880,2,208,5912,50186,236388,773040,1764000,2903040,3628800

%N Number of permutations p of {1,...,n} such that |p(i+1)-p(i)| < k, k=2,...,n; T(n,k), read by rows.

%H Li-yao Xia, <a href="/A249631/a249631.txt">Triangle of T(n,k) for n=2..10, k=2..n</a>

%e Triangle starts with n=2:

%e 2;

%e 2, 6;

%e 2, 12, 24;

%e 2, 20, 72, 120;

%e 2, 34, 180, 480, 720;

%o (Haskell) a n x = filter (\l -> all (< x) (zipWith (\x y -> abs (x - y)) l (tail l))) (permutations [1 .. n])

%o (PARI) isokp(perm, k) = {for (i=1, #perm-1, if (abs(perm[i]-perm[i+1]) >= k, return (0));); return (1);}

%o tabl(nn) = {for (n=2, nn, for (k=2, n, print1(sum(i=1, n!, isokp(numtoperm(n, i), k)), ", ");); print(););} \\ _Michel Marcus_, Nov 06 2014

%Y Cf. A000142, main diagonal, A062119, subdiagonal.

%Y Cf. A003274, A174700, A174701, A174702, 2nd to 5th columns, T(n,k), k=3,4,5,6.

%Y Cf. A174703, A174704, A174705, A174706, A174707, A174708, similar definitions.

%K nonn,tabl

%O 2,1

%A _Li-yao Xia_, Nov 02 2014